As one of the important factors influencing the ionospheric total electron content (TEC) estimation accuracy, receiver differential code biases (DCBs) should be properly removed from global navigation satellite system (GNSS) measurements. The intraday variability in receiver DCBs (rDCBs), which is usually ignored in the commonly used ionospheric observable retrieval procedure, has been identified as one of the major errors degrading the accuracy of TEC estimation. The modified carrier-to-code leveling (MCCL) method can be adopted to eliminate the impact of the rDCB variability on the retrieval of the ionospheric TEC from dual-frequency (DF) GNSS observations. In this contribution, we extend the MCCL method from two aspects. First, the DF MCCL method is adapted to the multi-frequency (MF) case, in which DF, triple-frequency or even arbitrary-frequency observations can be readily processed to simultaneously estimate both the ionospheric TEC and rDCB variations. Second, the MCCL method is refined to enable the handling of GLONASS data by accounting for the effects of code inter-frequency biases induced by the frequency division multiple access (FDMA) technology. Based on the test results, the retrieval accuracy of the ionospheric TEC using our proposed method can be improved from 9.47 TECu to 2.67 TECu in the presence of significant intraday rDCB variations. We discovered that the maximum difference in the rDCB variations of the same satellite system between different frequency bands can be as large as 10 ns. The dependence of multi-GNSS and MF rDCB variations on the ambient temperature is further verified in this study. The results show that the temperature dependence of rDCB varies among different satellite systems and frequency bands. Compared to the Galileo, GPS and GLONASS satellite systems, the Beidou system (BDS) rDCB estimates exhibit a stronger correlation with the measured temperature. The percentages of stations with the mean absolute Pearson correlation coefficient value above 0.8 are 27.17% for GPS, 30.58% for GLONASS, 43.78% for BDS and 33.9% for Galileo, respectively.

中文翻译：

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一种用于反演电离层 TEC 和接收器 DCB 日间变异性的多频和多 GNSS 方法

作为影响电离层总电子含量（TEC）估计精度的重要因素之一，接收器差分码偏差（DCB）应从全球导航卫星系统（GNSS）测量中适当去除。接收器 DCB (rDCB) 的日内变异在常用的电离层可观测反演程序中通常被忽略，已被确定为降低 TEC 估计精度的主要错误之一。可以采用改进的载波到码调平 (MCCL) 方法来消除 rDCB 可变性对从双频 (DF) GNSS 观测中反演电离层 TEC 的影响。在这个贡献中，我们从两个方面扩展了 MCCL 方法。首先，DF MCCL 方法适用于多频 (MF) 情况，其中 DF、可以很容易地处理三频甚至任意频率的观测，以同时估计电离层 TEC 和 rDCB 的变化。其次，MCCL 方法经过改进，通过考虑频分多址 (FDMA) 技术引起的代码频率间偏差的影响，能够处理 GLONASS 数据。根据测试结果，在存在显着的日内 rDCB 变化的情况下，使用我们提出的方法对电离层 TEC 的反演精度可以从 9.47 TECu 提高到 2.67 TECu。我们发现同一卫星系统不同频段之间rDCB变化的最大差异可以达到10 ns。本研究进一步验证了多 GNSS 和 MF rDCB 变化对环境温度的依赖性。结果表明，rDCB 的温度依赖性在不同的卫星系统和频段之间存在差异。与伽利略、GPS 和 GLONASS 卫星系统相比，北斗系统 (BDS) rDCB 估计值与测量的温度具有更强的相关性。平均绝对 Pearson 相关系数值高于 0.8 的站点百分比分别为 GPS 27.17%、GLONASS 30.58%、BDS 43.78% 和 Galileo 33.9%。